Essentially the same show as Cowboy BeBop just transposed into a different setting so it' s a toss up but the mix of accessible and satisfying story arcs, great sound design and top notch animation makes this one a perfect gateway anime to get folks interested in the medium.

2. Shigiru Death Frenzy

Such a perfect mix of explotation and art house. One of the more beautiful series I have seen (far exceeds "Kai Doh Maru").

3. Akira

The old stand by. Veers into incoherence so can be a bit of hard sell to some but the vision is so intensely realized it always has an impact.

Alternates would be:

Ninja Scroll movie (fun characters, great animation and lots of action)
Samurai X (big budget with classic storyline, lots of fun)
Last Exile (ditto)
Fist Of The North Star (low rent sure but a thoroughly enjoyable uptempo party anime)

My wife would probably add Fruits Basket to the list (frenetic and silly).

[...] None of the 3 would ever work if you tried doing a live action version of them.

I love Cowboy Bebop too but there is pretty much nothing about that anime that really requires the space theme (as shown by "Samurai Champloo"). Even with the space theme it should be doable as long as you go the "Sky Captain and the World Of Tomorrow" route of all green screen.

On a story and character level the feel of Cowboy Bebop is pretty close to "Yojimbo" which was made decades ago (and likely acted as partial inspiration).

Everyone knows dragon ball z
Nobody in this world would know any other Japanese cartoon seriously only anime fans would know
Regular people that like rap and socialize like dragon ball z and naruto and sum what bleach
One piece is terrible n my opinion and friends.